Resolução de problemas: uma discussão sobre o ensino de análise combinatória

Abstract

This work aimed to investigate a proposal for teaching that uses as a teaching tool to the History of Mathematics and Problem Solving, for the teaching and learning of Combinatorial Analysis, subject usually treated in the 2nd year of High School. In its turn, the Combinatorial Analysis aims to establish counting methods, or more simply, counting problems, and is considered as one of the issues of greatest difficulty. For the realization of that done, we seek in literature authors who are favorable the use of History in the teaching and learning of mathematics and its main arguments, authors who believe in the effectiveness of teaching and learning with the Problem Solving and finally we emphasize the contributions from works or texts on the History of Mathematics. The present work aimed to improve the teaching and learning of Combinatorial Analysis; lastly, bring a Mathematic more humanized, related with historical facts and with real-world applications. Then this work was applied to a class of High School, in a public school of the State of Rio de Janeiro and analyzed. We found that the content was assimilated easily and there was a better exploitation of the students. We hope that, from this work, the study of Combinatorial Analysis, there is a better understanding of this subject of Mathematics. Still based in the dissertation we prepared book with the title: “The Combinatorial Analysis Developed with Historical Aspects”, which is the educational product, where we established combinatorial concepts through historical facts and problems. The greatest difficulty we had was the lack of work specifically relate to the History of Combinatorial Analysis.